Related papers: Formal confluence of quantum differential operator…
Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…
In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.
In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states,…
We introduce a twisted quantum affine algebra associated to each simply laced finite dimensional simple Lie algebra. This new algebra is a Hopf algebra with a Drinfeld-type comultiplication. We obtain this algebra by considering its vertex…
In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid…
We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The…
A straightforward argument shows that, by allowing counterfactual elements of physical reality, any arbitrary discrete finite-dimensional operator corresponds to an observable.
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…
A general procedure is introduced allowing for the infinite decomposition of nonlocal operators off the light--cone into operators of definite geometric twist.
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain…
Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which…
We examine how to distinguish between unitary operators, when the exact form of the possible operators is not known. Instead we are supplied with "programs" in the form of unitary transforms, which can be used as references for identifying…
Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty$ are not singular critical points of…
The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for…
A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a…
We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra. Furthermore, the connection…